On linearization of the Boltzmann equation
作者:
F. Chvála,
期刊:
Transport Theory and Statistical Physics
(Taylor Available online 1998)
卷期:
Volume 27,
issue 3-4
页码: 383-393
ISSN:0041-1450
年代: 1998
DOI:10.1080/00411459808205633
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
The velocity distribution function for particles of a spatially inhomogencous gas confined in a vessel is considered as a solution of the nonlinear Boltzmann kinetic equation. Finite collision frequency is assumed. An external potential force acting upon the particles is imposed, an initial condition is given, and the interaction between the particles of the gas and the walls of the vessel is represented by a short-ranging repulsive potential force acting within a neighbourhood of the walls of the vessel. The linearization of the problem is studied, including the cases the solution cannot be approximated by a Maxwellian distribution. A sequence{fj}of iterations is constructed such thatfj+1is a solution of the problem linearized aroundfj. It is proved that the iterations converge in a convenient Banach function space to the mild solution of the original nonlinear problem provided the initial approximation is chosen close enough to the solution, and an estimate of the convergence rale is found.
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